Optical System Determination According to Advanced Criteria

ABSTRACT

A method implemented by computer means for calculating by optimization an optical system for example an ophthalmic lens according to at least one criterion among the following list consisting of: ocular deviation, object visual angular field in central vision, image visual angular field in central vision, pupil field ray deviation, object visual angular field in peripheral vision, image visual angular field in peripheral vision, prismatic deviation in peripheral vision, magnification in peripheral vision, lens volume, magnification of the eyes, temple shift, or a variation of preceding criteria.

RELATED APPLICATIONS

This is a U.S. National Phase Application under 35 USC 371 ofInternational Application PCT/EP2009/063569 filed on Oct. 16, 2009.

This Application claims the priority of European Application No.08305693.7 filed Oct. 16, 2008, the entire content of which is herebyincorporated by reference.

FIELD OF THE INVENTION

The invention relates to a method for calculating by optimization anoptical system, for example and not limitedly the optical systemrepresents an ophthalmic lens. More specifically, the invention relatesto a method for determining parameters of an optical system implementingan optimization of criteria.

BACKGROUND OF THE INVENTION

Optimization methods for optical system calculation are well known;however, currently the number of criteria taken into account is limitedand do not enable to answer all lens wearer needs. French patent FR9812109 of the Applicant describes for example a method for determiningoptimal parameters for an optical system according especially toastigmatism and power criteria.

Known methods present drawbacks arising from the fact that classicalcriteria aim at improving only optical quality of the image caused byoptical aberrations like power and astigmatism errors. These aberrationsinduce blurring in the image and a drop in contrast, causing thereforeunclear vision.

Classical criteria do not enable to improve other kind of performancesuch as image deformations and localisation which are main issues forenhancing wearer adaptation and answering user specific needs ingeneral.

SUMMARY OF THE INVENTION

The present invention makes it possible to consider a large number ofcriteria in order to achieve a better optical system calculation, closerto the user needs.

Thereby, one aspect of the invention is directed to a method forcalculating by optimization an optical system for example an ophthalmiclens according to at least one criterion comprising the steps of:

-   -   i. Selecting at least one criterion among one or several of the        three following criteria groups consisting of:    -   central vision criteria group consisting of: ocular deviation,        object visual angular field in central vision, image visual        angular field in central vision, or a variation of preceding        criteria;    -   peripheral vision criteria group consisting of: pupil field ray        deviation, object visual angular field in peripheral vision,        image visual angular field in peripheral vision, prismatic        deviation in peripheral vision, magnification in peripheral        vision, or a variation of preceding criteria;    -   general criteria group consisting of: lens volume, magnification        of the eye, temple shift;    -   ii. For each selected criterion, defining:    -   an evaluation zone comprising one or several evaluation domains        and a set of target values associated to said evaluation        domains, if said criterion belongs to the central or to the        peripheral vision criteria groups, or    -   a target value associated to said criterion, if said criterion        belongs to the general criteria group;    -   iii. Selecting a starting optical system and defining a working        optical system to be equal to the starting optical system, where        the starting optical system and the working optical system        comprise each at least two optical surfaces;    -   iv. Evaluating for the working optical system and for each        selected criterion:    -   a set of criterion values associated to said evaluation domains,        if said selected criterion belongs to the central or peripheral        vision criteria groups, or    -   a criterion value, if said criterion belongs to the general        criteria group;    -   v. Modifying at least one parameter of the working optical        system, in order to minimize a cost function considering target        values and criterion values by repeating step iv till a stop        criterion is satisfied.

The criteria disclosed herein enable the optical designer to betteranswer lens wearer needs. For example, image visual angular field incentral vision is to be optimized according to specific needs andametropia in order, for example, to limit space scrolling. Anotheradvantage of the method is the possibility to optimize the object visualangular field in central vision in order to adapt the latter to thewearer or to the frame of its glasses; for example, thanks to themethod, the optical designer will try to widen object visual angularfield for wearers suffering from hypermetropia since hypermetropicwearers are always complaining of a narrow field of view.

The choice of here above mentioned criteria chosen among one or severalof the criteria groups allow to manage shape deformations of the imageand deviations (ocular and/or prismatic) whereas criteria commonly usedto determine optical systems are directed to optical aberrationsmanagement.

Optical aberrations cause blurring the image and reduce contrast and/orcause unclear vision whereas shape deformations of the image anddeviations (ocular and/or prismatic) modify the appearance of the objectto be seen, and the image of the object to be seen may be smaller orbigger, twisted, delocalized compared to the actual object to be seen.

According to an embodiment, the method is implemented by technicalmeans, as for example by computer means.

According to different embodiments, that can be combined, the at leastone criterion selected among the criteria group is:

-   -   one or several central vision criteria,    -   one or several peripheral vision criteria,    -   one or several general criteria.

According to different embodiments that can be combined, the at leastone selected criterion among the criteria groups is selected among oneor a plurality of following sub-groups:

-   -   central vision criteria sub-group 1 consisting of ocular        deviation, or a variation thereof;    -   central vision criteria sub-group 2 consisting of object visual        angular field in central vision, image visual angular field in        central vision or a variation thereof;    -   peripheral vision criteria sub-group 1 consisting of pupil field        ray deviation, prismatic deviation in peripheral vision or a        variation thereof;    -   peripheral vision criteria sub-group 2 consisting of object        visual angular field in peripheral vision, image vision angular        field in peripheral vision or a variation thereof;    -   peripheral vision criteria sub-group 3 consisting of        magnification in peripheral vision or a variation thereof;    -   general criteria sub-group 1 consisting of lens volume or a        variation thereof;    -   general criteria sub-group 2 consisting of magnification of the        eye, temple shift or a variation thereof.

In the scope of the present invention, the aforementioned terms areunderstood according to the following definitions:

-   -   An optical system is defined by the coefficients of the        equations of all its surfaces, the index of the glasses and the        position of each surface relatively to each other (offset,        rotation and tilt). These elements are referred as the        parameters of the optical system. Surfaces of an optical system        are usually represented according to a polynomial or parametric        equation obtained by using a model based on the B-splines or        Zernike polynomials. These models give continuous curvature on        the whole lens. Surfaces can also be Fresnel or pixelized        surfaces. The index of materials can be inhomogeneous and depend        on some parameters of the optical system.    -   Central vision (also referred as foveal vision) describes the        work of the fovea, a small area in the center of the retina that        contains a rich collection of cones. In a central vision        situation, an observer looks at an object which stays in a gaze        direction and the fovea of the observer is moved to follow the        object. Central vision permits a person to read, drive, and        perform other activities that require fine and sharp vision.    -   A gaze direction is defined by two angles measured with regard        to reference axes centered on the center of rotation of the eye.    -   Peripheral vision describes the ability to see objects and        movement outside of the direct line of vision. In a peripheral        vision situation, an observer looks in a fixed gaze direction        and an object is seen out of this direct line of vision. The        direction of a ray coming from the object to the eye is then        different from the gaze direction and is referred as peripheral        ray direction. Peripheral vision is the work of the rods, nerve        cells located outside the fovea of the retina.    -   A peripheral ray direction is defined by two angles measured        with regard to reference axes centered on the eye entrance pupil        and moving along the gaze direction axis.    -   Ocular deviation is defined in central vision and describes the        fact that adding a lens causes an eye to rotate in order to stay        focused on the same object. The angle can be measured in        prismatic diopters.    -   Object visual angular field in central vision is defined in the        object space by the angular portion of space that the eye can        observe scanning an angular portion of the lens determined by at        least two gaze directions. For instance, these gaze directions        can be defined by the shape of the spectacle frame or by an        aberration level that hinders visualizing the object space with        a good enough sharpness.    -   Image visual angular field in central vision in the image space        (eye space) is defined for a determined and fixed object visual        angular field in central vision in the object space, as the        angular portion scanned by the eye to visualize the visual        angular field in the object space.    -   Variation of a criterion evaluated thanks to an evaluation        function in a particular gaze direction (α₁/β₁) according to a        component of the gaze direction is understood as the derivative        of the said evaluation function of the said criterion with        respect to the said component. Considering a evaluation function        H_(k), one can consider the partial derivative of H_(k) with        respect to α:

$\frac{\partial H_{k}}{\partial\alpha}{\left( {\alpha_{1},\beta_{1}} \right).}$

One can consider the partial derivative of H_(k) with respect to β:

$\frac{\partial H_{k}}{\partial\beta}{\left( {\alpha_{1},\beta_{1}} \right).}$

Variation of a criteria can be evaluated as the composition of thepartial derivatives of the evaluation function with respect to α and toβ, as for example:

$\sqrt{\left( {\frac{\partial H_{k}}{\partial\alpha}\left( {\alpha_{1},\beta_{1}} \right)} \right)^{2} + \left( {\frac{\partial H_{k}}{\partial\beta}\left( {\alpha_{1},\beta_{1}} \right)} \right)^{2}}$

-   -   Pupil field ray deviation describes that a ray coming from an        object located in the peripheral field of view is modified by        adding a lens on its path to the eye entrance pupil.    -   Object visual angular field in peripheral vision is defined in        the object space. It is the angular portion of space that the        eye can observe in the peripheral visual angular field of view        (while the eye is looking in a fixed direction) defined by at        least two rays issued from the center of eye entrance pupil. For        instance, these rays can be defined by the shape of the        spectacle frame or by an aberration level that hinders        visualizing the object space with a good enough sharpness.    -   Image visual angular field in peripheral vision is defined for a        determined and fixed peripheral object visual angular field as        the corresponding angular portion in the image space viewed by        the peripheral vision of the eye.    -   Prismatic deviation in peripheral vision is defined in the        object space by the angular deviation of a ray issued from the        center of the entrance pupil introduced by the quantity of prism        of the lens.    -   Magnification in peripheral vision is defined as the ratio        between the apparent angular size (or the solid angle) of an        object seen in peripheral vision without lens and the apparent        angular size (or the solid angle) of an object seen through the        lens in peripheral vision.    -   Variation of a criterion evaluated thanks to an evaluation        function in a particular ray direction (α′₁, β′₁) according to a        component of the ray direction is understood as the derivative        of the said evaluation function of the said criterion with        respect to the said component. Considering a evaluation function        H_(k), one can consider the partial derivative of H_(k) with        respect to α′:

$\frac{\partial H_{k}}{\partial\alpha^{\prime}}{\left( {\alpha_{1}^{\prime},\beta_{1}^{\prime}} \right).}$

One can consider the partial derivative of H_(k) with respect to β′:

$\frac{\partial H_{k}}{\partial\beta^{\prime}}{\left( {\alpha_{1}^{\prime},\beta_{1}^{\prime}} \right).}$

Variation of a criteria can be evaluated as the composition of thepartial derivatives of the evaluation function with respect to α′ and toβ′, as for example:

$\sqrt{\left( {\frac{\partial H_{k}}{\partial\alpha^{\prime}}\left( {\alpha_{1}^{\prime},\beta_{1}^{\prime}} \right)} \right)^{2} + \left( {\frac{\partial H_{k}}{\partial\beta^{\prime}}\left( {\alpha_{1}^{\prime},\beta_{1}^{\prime}} \right)} \right)^{2}}$

-   -   Magnification of the eye is defined as the magnification of the        eye of the wearer assessed by an observer.    -   Temple shift is defined as the offset of the wearer temple        assessed by an observer.    -   Lens volume is the volume of the lens. It can be assessed        through discretization of the lens, for example by a trapezium        method or by a rectangle method.    -   An evaluation zone is associated with a criterion belonging to        the central or peripheral vision criteria groups to be        evaluated; it is composed of one or several evaluation domains.        An evaluation domain is composed of one or several gaze        directions for a criterion belonging to the central vision        criteria group and of one or several peripheral ray directions        for a criterion belonging to the peripheral vision criteria        group.    -   A set is defined as one or several entities.    -   A target value is a value to be reached by a criterion. When the        selected criterion belongs to the central or peripheral vision        criteria groups, a target value is associated to an evaluation        domain.    -   The starting optical system is defined as a set of initial        parameters of the optical system to be optimized.    -   The working optical system is defined as a set of parameters        representing an optical system. At the beginning of the        optimization process, the working optical system parameters are        equal to the parameters of the starting optical system. The        working optical system parameters are then modified through the        optimization process.    -   A stop criterion is used to identify the best iteration to stop        the optimization algorithm. It can be for example a threshold on        the cost function: ∥J(v)∥<ε₁ which indicates that the lens v is        close enough to the solution. It can also be a criterion on the        relative variation of the cost function between two iterations k        and k+1: ∥J(v^(k+1))−J(v^(k))∥<ε₂∥J(v^(k))∥ which indicates a        stagnation of the algorithm.

Criterion values can be evaluated considering the working optical systemparameters. According to an embodiment, criteria are evaluated throughray tracing.

According to an embodiment, an evaluation function associates acriterion value to a criterion belonging to the criteria groups, anevaluation domain for criterion chosen among central and peripheralvision criterion groups, and an optical system.

The cost function provides a level of performance of the working opticalsystem according to the target values and to the criterion valuesevaluated for the working optical system parameters.

In one embodiment the cost function is a sum over the selected criteriaof:

-   -   sums, over the evaluation domains, of differences between a        criterion value associated to an evaluation domain and the        target value associated to said evaluation domain to the power        of two, for criteria belonging to the central vision and        peripheral vision criteria groups, and    -   differences between a criterion value and a target value to the        power of two, for criteria belonging to the general criteria        group.

In one embodiment the working optical system to be optimized comprisesat least two optical surfaces and the parameter which is modified is atleast the coefficient of the equation of one optical surface of theworking optical system.

In one embodiment wherein a selected criterion belongs to the centralvision criteria group, the associated evaluation domains comprise atleast one gaze direction, said direction being considered with regard toreference axes associated with the eye rotation center and being used toperform ray tracing from the eye rotation center for the criterionevaluation.

In one embodiment wherein a selected criterion belongs to peripheralvision criteria group, the associated evaluation domains comprise of atleast one peripheral ray direction, said direction being considered withregard to reference axes associated with the entrance pupil centermoving along a determined gaze direction and being used to perform raytracing from the entrance pupil center for the criterion evaluation.

In one embodiment wherein a selected criterion belongs to any of: oculardeviation, pupil field ray deviation, prismatic deviation in peripheralvision, magnification in peripheral vision, the associated evaluationdomains consist in one direction.

This direction refers to a peripheral ray direction for a criterionbelonging to the peripheral criteria group and to a gaze direction for acriterion belonging to the central vision criteria group.

In one embodiment wherein a selected criterion belongs to any of objectvisual angular field in central vision, image visual angular field incentral vision, object visual angular field in peripheral vision andimage visual angular field in peripheral vision, the associatedevaluation domains comprise of at least two directions.

-   -   In one embodiment the selected criterion is defined either by a        variation of a criterion belonging to the central vision        criteria group or by a variation of a criterion belonging to the        peripheral vision criteria group.    -   In one embodiment, the working optical system to be optimized        comprises at least two optical surfaces and the parameters which        are modified are at least the coefficients of the equations of        two optical surfaces of the working optical system.

It is generally difficult to optimize a lens considering a lot ofcriteria which are from different natures if only the equation of onesurface is considered as variable. This embodiment enables opticaldesigners to take into account a larger number of criteria in theoptimization process and is paving the way for optical systemgeometrical performance enhancement and better answer to physiologicalneeds of lens wearers. The benefit for the wearer is improved whenseveral surfaces of the optical system are simultaneously optimized.

In one embodiment wherein the optical system to be optimized comprisesat least two optical surfaces, the modification of the working opticalsystem is operated in modifying at least the index of the workingoptical system. It is possible to make a lens from some inhomogeneousmaterial, one where there is a Gradient in the Index of refraction(known as GRIN lens). For example, the distribution of the index whichis optimized can be axial or radial and/or can depend on the wavelength.

In one embodiment, the method for calculating an optical system furthercomprises astigmatism criterion in central vision and/or power criterionin central vision. Power criterion in central vision means that thepower prescribed to the wearer is taken into account. During theoptimization, parameters of the optical system are calculated in orderto minimize power errors for each gaze direction.Astigmatism criterion in central vision means that during theoptimization, parameters of the optical system are calculated in orderto minimize the difference between astigmatism prescribed to the wearerand astigmatism generated by the working optical system both as regardsamplitude and the axis thereof in the reference axes associated to theCRE and for each gaze direction, this difference being called residualastigmatism. The French patent FR 9812109 of the Applicant describes howto take into account such classical criteria during an optical systemoptimization method.

In one embodiment, the optical system is a progressive addition lens andthe method for calculating an optical system further comprises add powercriterion in central vision.

In one embodiment, the cost function J is mathematically expressedaccording to:

${{J(v)} = {{\sum\limits_{k = 1}^{N\; 1}{\sum\limits_{i = 1}^{Mk}{w_{k}^{i}*\left( {{H_{k}\left( {D_{k}^{i},v} \right)} - T_{k}^{i}} \right)^{2}}}} + {\sum\limits_{k = 1}^{N\; 2}{w_{k}^{\prime}*\left( {{H_{k}^{\prime}(v)} - T_{k}^{\prime}} \right)^{2}}}}},$

wherein:k and i are integer variables,N₁ is an integer superior or equal to 1 and represents the number ofselected criteria belonging to the central vision and peripheral visioncriteria groups;N₂ is an integer superior or equal to 1 and represents the number ofselected criteria belonging to the general criteria group;M_(k) is an integer superior or equal to 1 and represents the number ofevaluation domains for a criterion belonging to the central vision orperipheral vision criteria groups of index k;v defines the working optical system parameters;w^(i) _(k) are the weights associated to a criterion belonging to thecentral vision or peripheral vision criteria groups of index k and to anassociated evaluation domain of index i;w′_(k) is the weight associated to a criterion belonging to the generalcriteria group of index kD^(i) _(k) is an evaluation domain of index i of an evaluation zoneassociated to a criterion belonging to the central vision or peripheralvision criteria groups of index k;H_(k) is an evaluation function which associates a criterion value to acriterion belonging to the central vision or peripheral vision criteriagroups of index k, an evaluation domain D^(i) _(k) and a optical systemdefined by its parameters v;H′_(k) is an evaluation function which associates a criterion value to acriterion belonging to the general criteria group of index k and aoptical system defined by its parameters v;T^(i) _(k) is a target value of index i of the set of target valuesassociated to an evaluation domain D^(i) _(k) of a criterion belongingto the central vision or peripheral vision criteria groups of index k;T′_(k) is the target value associated to a criterion belonging to thegeneral criteria group of index k.

In one embodiment, the invention also relates to a method ofmanufacturing a lens according to an optical system, the methodcomprising the steps of:

-   -   calculating by optimization the optical system according to the        method described hereinabove,    -   surface machining of at least one optical surface according to        said optical system.

When both surfaces of a lens are optimized during the process, themanufacturing method relates to surface machining both surfaces.

Another aspect of the invention relates to a computer program productcomprising one or more stored sequences of instructions that isaccessible to a processor and which, when executed by the processor,causes the processor to carry out the steps of the different embodimentsof the preceding methods.

Another aspect of the invention relates to a computer-readable mediumcarrying one or more sequences of instructions of the preceding computerprogram product.

Unless specifically stated otherwise, as apparent from the followingdiscussions, it is appreciated that throughout the specificationdiscussions utilizing terms such as “evaluating”, “computing”,“calculating” “generating”, or the like, refer to the action and/orprocesses of a computer or computing system, or similar electroniccomputing device, that manipulate and/or transform data represented asphysical, such as electronic, quantities within the computing system'sregisters and/or memories into other data similarly represented asphysical quantities within the computing system's memories, registers orother such information storage, transmission or display devices.

Embodiments of the present invention may include apparatuses forperforming the operations herein. This apparatus may be speciallyconstructed for the desired purposes, or it may comprise a generalpurpose computer or Digital Signal Processor (“DSP”) selectivelyactivated or reconfigured by a computer program stored in the computer.Such a computer program may be stored in a computer readable storagemedium, such as, but is not limited to, any type of disk includingfloppy disks, optical disks, CD-ROMs, magnetic-optical disks, read-onlymemories (ROMs), random access memories (RAMs) electrically programmableread-only memories (EPROMs), electrically erasable and programmable readonly memories (EEPROMs), magnetic or optical cards, or any other type ofmedia suitable for storing electronic instructions, and capable of beingcoupled to a computer system bus.

The processes and displays presented herein are not inherently relatedto any particular computer or other apparatus. Various general purposesystems may be used with programs in accordance with the teachingsherein, or it may prove convenient to construct a more specializedapparatus to perform the desired method. The desired structure for avariety of these systems will appear from the description below. Inaddition, embodiments of the present invention are not described withreference to any particular programming language. It will be appreciatedthat a variety of programming languages may be used to implement theteachings of the inventions as described herein.

BRIEF DESCRIPTION OF THE DRAWINGS

Non limited embodiments of the invention will now be described withreference to the accompanying drawing wherein FIGS. 1 to 12 describeexamples of criteria evaluation according to embodiments of the presentinvention. Those figures describe non limiting examples, same referenceon different figures refer to the same object.

FIG. 1 shows a schematic view of a lens plus eye system.

FIG. 2 shows a ray tracing from the center of rotation of the eye.

FIG. 3 shows a ray tracing from the center of the eye entrance pupil.

FIG. 4 illustrates prismatic deviation in peripheral vision.

FIG. 5 illustrates ocular deviation.

FIG. 6 illustrates pupil ray field deviation.

FIG. 7 illustrates object visual angular field in central vision.

FIG. 8 illustrates horizontal object visual angular field.

FIG. 9 illustrates horizontal prismatic deviation in central vision.

FIG. 10 illustrates total object visual angular field.

FIG. 11 illustrates image visual angular field in central vision.

FIG. 12 illustrates object visual angular field in peripheral vision.

FIG. 13 illustrates image visual angular field in peripheral vision.

FIG. 14 illustrates the magnification of the eye in an embodiment of theinvention.

FIG. 15 a and b illustrate temple shift in an embodiment of the presentinvention.

DESCRIPTION OF PREFERRED EMBODIMENTS

Skilled artisans appreciate that elements in the figures are illustratedfor simplicity and clarity and have not necessarily been drawn to scale.For example, the dimensions of some of the elements in the figures maybe exaggerated relative to other elements to help improve theunderstanding of the embodiments of the present invention.

We focus first on the criterion evaluation method according to thevision situation (central or peripheral). In order to compute acriterion, ray tracing software can be used. Ray tracing has specialfeatures according to the model of the lens-plus-eye system.

FIG. 1 illustrates a schematic view of a lens-plus-eye system. Referringto FIG. 1, an eye position can be defined by the center of rotation ofthe eye CRE and the entrance pupil central point P. PS is the pupil size(not drawn to scale). The distance q′ between the CRE and the lens 20 isgenerally, but not limited to, set to 25.5 mm, and p′ defines theposition of the eye entrance pupil with respect to the CRE.

FIG. 2 illustrates a model for central vision in the purpose ofassessing a criterion in a central vision situation by ray tracing. In acentral vision situation, the eye rotates about its center of rotationas well as the entrance pupil of the eye. A gaze direction is defined bytwo angles (α,β) measured with regard to reference axes R=(X,Y,Z)centered on the CRE. For assessing a central vision criterion in a gazedirection (α,β), a gaze ray 1 is built from the CRE in the gazedirection (α,β). 11 is the incident ray after passing through the lens20.

FIG. 3 illustrates a model for peripheral vision in the purpose ofassessing a criterion in a peripheral vision situation through raytracing. In a peripheral vision situation, a gaze direction (α,β) (notrepresented here) is fixed, and an object is viewed in a peripheral raydirection different from the gaze direction. A peripheral ray directionis defined by two angles (α′,β′) measured with regard to reference axesR′=(X′,Y′,Z′) centered on the eye entrance pupil and moving along thegaze direction axis given by the fixed direction (α,β) and representedby axis X′ on FIG. 3. For assessing a peripheral vision criterion in aperipheral ray direction (α′,β3′), a peripheral ray 2 is built from thecenter of the pupil P in a peripheral ray direction (α′,β′). 22 is theincident ray after passing through the lens 20.

According to the gaze ray 1 (in central vision) or to the peripheral ray2 (in peripheral vision), the ray-tracing software computes thecorresponding incident ray, alternatively under reference 11 and 22 onFIGS. 2 and 3. Then, an object point is chosen on the ray in the objectspace and from this object a pencil of rays is built to calculate thefinal image. Ray tracing enables then to compute the selected criteria.

FIGS. 4 to 12 are now illustrating the criterion evaluation method ofcriteria according to the present invention.

FIG. 4 illustrates ray tracing for estimating prismatic deviation PD inperipheral vision. Prismatic deviation in peripheral vision is estimatedthrough ray tracing of a peripheral ray associated to a peripheral raydirection (α′,β′) given with regard to reference axes centered on thecenter of the entrance pupil and moving along the gaze direction, asdiscussed hereinabove. A ray 2 issued from the center of the entrancepupil in peripheral ray direction (α′,β′) with the gaze direction axisX′ is traced. Incident ray 22 corresponding to ray 2 is then built.Prismatic deviation represents the angle between incident ray 22 and avirtual ray 3 issued from the center of the pupil in the direction ofray 2 and not deviated by the prism of lens 20.

FIG. 5 describes ocular deviation OCD. It shows a first ray 33 comingfrom an object 10 when no lens is placed in its path to the CRE, and asecond ray 120 coming from the same object whose path is modified by theaddition of a lens 20. Ray 12 corresponds to ray 120 in the image spaceafter passing through the lens 20. The ocular deviation OCD in adirection (α,β) is estimated in central vision and is defined as theangle between:

-   -   the direction of the eye targeting an object without lens        (represented by ray 33) and    -   the direction of the eye targeting the same object when said        lens is placed in front of the viewer eyes (represented by ray        12).        As an example, an evaluation function is programmed to evaluate        the criterion OCD.

${{OCD}} = {{{H\left( {D,v} \right)}} = {{Arcsin}\left( \frac{{V_{ini}\bigwedge V_{fin}}}{{V_{ini}} \cdot {V_{fin}}} \right)}}$

whereV_(ini) and V_(fin) are direction vectors of alternatively ray 33 andray 12.The evaluation domain is composed of two gaze directions D={(αi,βi),i=1,2} (α1,β1) corresponding to ray 33, and (α2,β2) corresponding to ray12.

FIG. 6 illustrates pupil ray field deviation PRFD, it shows a first ray34 coming from an object 10 located in the peripheral field of view whenno lens is placed in its path to the eye entrance pupil, and a secondincident ray 230 coming from the same object whose path is modified bythe introduction of a lens 20. Ray 23 corresponds in the image field toincident ray 230.

Pupil field ray deviation PRFD is estimated in peripheral vision and isdefined as the angle, measured in the image space, between

-   -   a straight ray 34 coming from an object localised in the        peripheral field of view of an eye and entering the center of        the pupil, and    -   a ray 23 coming from the same object and entering the center of        the pupil when said lens is placed on the eyes of the wearer.        As an example, an evaluation function is programmed to evaluate        the criterion PRFD.

${PRFD} = {{H\left( {D,v} \right)} = {{Arcsin}\left( \frac{{V_{ini}\bigwedge V_{fin}}}{{V_{ini}} \cdot {V_{fin}}} \right)}}$

whereV_(ini) and V_(fin) are direction vectors of respectively ray 34 and ray23.The evaluation domain is composed of two gaze directionsD={(αi,βi),i=1,2} (α1,β1) corresponding to ray 34, and (α2,β2)corresponding to ray 23.

FIG. 7 illustrates object visual angular field in central vision in aplane and for two arbitrarily chosen rays 4 and 5 issued from the CRE.The object visual angular field represents the angular portion of spacethat the eye can observe scanning an angular portion of the lensdetermined by ray 4 and ray 5 in the object space. The hatched part 60represents the object visual angular field in central vision.

FIG. 8 illustrates an example of visual angular field VF in centralvision for two rays 41 and 51 issued from the CRE. The lens 20 isrepresented as a surface with isoastigmatism lines 201-206. Rays 41 and51 are defined as the intersection between a predetermined horizontalaxis given by a direction α and two predetermined isoastigmatism lines201 and 204. These intersections enable to trace ray 41 along direction(α, β1) and ray 51 along direction (α,β2). The object visual angularfield VF in central vision is a function of prismatic deviation and canbe mathematically expressed for two rays as:

VF(α)=|β1+Dp _(—) H(α,β1)|+|β2+Dp _(—) H(α,β2)|

-   -   Dp_H(α,β1) represents horizontal prismatic deviation in the gaze        direction (α,β1). Horizontal prismatic deviation is the        component of the prismatic deviation in an horizontal plane        referenced P on FIG. 8.    -   Dp_H(α,β2) represents horizontal prismatic deviation in the gaze        direction (α,β2).    -   D={(α,β1),(α,β2)} is an evaluation domain. An evaluation        function associated with the criterion visual angular field is        given by H(D,v)=VF(α) for given optical system parameters v.

FIG. 9 illustrates horizontal prismatic deviation HPD in central vision.Prismatic deviation is defined as the angular difference between ray 130and ray 35. Ray 130 is the image of the ray 13 in the object space. Ray13 is issued from the eye rotation center according to direction (α,β)in the fixed reference axes (X,Y,Z) centered on the eye rotation centeras represented on FIG. 9. Ray 35 is a virtual ray issued from the eyerotation center according to direction (α,β) and not deviated by theprism of the lens. Horizontal prismatic deviation HPD is the componentof the prismatic deviation in the plane (XOZ) and can be calculatedthrough:

${{HPD} = \left( {{Arcsin}\left( {\left( \frac{V_{ini}^{h}\bigwedge V_{fin}^{h}}{{V_{ini}^{h}}{V_{fin}^{h}}} \right) \cdot \overset{\rightarrow}{y}} \right)} \right)},$

wherein V^(h)=V−{right arrow over (y)}(V·{right arrow over (y)}), andV_(ini) and V_(fin) are direction vectors of alternatively ray 13 and130.

An evaluation domain is composed of one gaze direction D={(α,β)}, (α, β)corresponding to ray 13 and an evaluation function is given byH(D,v)=HPD.

FIG. 10 illustrates another embodiment of object visual angular field incentral vision defined by a set of gaze directions representing thespectacle frame shape 210. The lens 20 is represented as a surface withisoastigmatism lines 201-208. For each (αi,βi) of said gaze directions,we define Pi the plane containing:

-   -   the vector defined by the gaze direction (αi,βi)    -   the vector defined by the gaze direction (0,0)    -   the Centre of Rotation of the Eye        We calculate the prismatic deviation projected on Pi for the        gaze direction given by (α,β)=(0,0): Dp_i(0,0).        We calculate the prismatic deviation projected on Pi for the        gaze direction given by (αi,βi):Dp_i(αi,βi).        This visual angular field is named total object visual angular        field and can be mathematically expressed as

${VF} = {\sum\limits_{i}{{{{Dp\_ i}\left( {0,0} \right)} + {\beta \; i} + {{Dp\_ i}\left( {{\alpha \; i},{\beta \; i}} \right)}}}}$

Where:

-   -   Dp_i(αi,βi) represents the prismatic deviation in the gaze        direction (αi,βi) projected on the plane Pi.    -   Let D be the evaluation domain composed by the said gaze        directions D={(αi,βi)}. An evaluation function associated to the        criterion object visual angular field and the evaluation domain        D1 is given by H(D1,v)=VF

FIG. 11 illustrates image visual angular field in central vision, rays 4and 5 are used to define the object visual angular field in centralvision and dotted part 70 represents the image visual angular field incentral vision considering an object visual angular field in centralvision represented in hatched part 60.

FIG. 12 illustrates object visual angular field in peripheral vision ina plane and for two arbitrarily chosen rays 6 and 7 issued from theentrance pupil of the eye P. The hatched part 80 represents the objectvisual angular field in peripheral vision.

FIG. 13 illustrates image visual angular field in peripheral vision,rays 6 and 7 are used to define the object visual angular field inperipheral vision 80 and dotted part 90 represents the image visualangular field in peripheral vision considering an object visual angularfield in peripheral vision represented in hatched part 80.

FIG. 14 illustrates the magnification of the eye ME of a wearer. Ω andΩ′ are alternately the solid angles under which an observer sees the eyeof a wearer with and without a lens 20. The observer is located at adistance d of the wearer which eye is referred as 21, the center of theobserver entrance pupil is referred as OP and the vertex distancebetween the wearer's eye 21 and the lens 20 is referred as q′. Forexample, the distance d can be equal to one meter.

This criterion can be mathematically expressed as

${ME} = {\frac{\Omega}{\Omega^{\prime}}.}$

An evaluation function can be the mean value of ME criteria valuescalculated for n positions of the observer:

${H(v)} = {\frac{1}{n}{\sum\limits_{i = 1}^{n}{\frac{\Omega_{i}}{\Omega_{i}^{\prime}}.}}}$

FIGS. 15 a and b illustrate temple shift TS.

Temple shift is due to the prismatic deviation induced by a lens 20 whena wearer is seen by an observer. OP is the pupil center point of anobserver looking the wearer's head 25. The wearer's eye is referred as21, the wearer's nose is referred as 27, the wearer's temple is referredas 26. The wearer is wearing spectacle lenses. Temple shift is definedas an angle TS between a ray 100 stemmed from the temple 26 when theobserver is looking the temple of the wearer without the lens and a ray101 stemmed from the temple 26 when the observer is looking the templeof the wearer through the lens 20. For example, the distance between thewearer and the observer can be equal to one meter.

Non limiting embodiments of the cost function are now described.

We now refer to an embodiment of the invention in which the selectedcriteria belong to the central and peripheral criteria groups and thecost function can be defined as a sum, over a set of selected criteria(C₁, . . . C_(N1)), of each selected criterion cost function.

For a selected criterion C_(k) (kε[1 . . . N₁], N₁ integer superior orequal to 1), in order to define a criterion cost function, we furtherdevelop the expression of the criterion values.

An evaluation zone D_(k) is associated to a criterion C_(k). Theevaluation zone comprises one or several evaluation domain D^(i) _(k),(iε[1 . . . M_(k)], M_(k) integer superior or equal to 1 represents thenumber of evaluation domains associated to a criterion, said evaluationdomain being defined as at least one gaze direction (α,β) if saidcriterion belongs to the central vision criteria group, or at least oneperipheral ray direction (α′,β′) if said criterion belongs to theperipheral vision criteria group.

For a criterion C_(k) and an evaluation zone D_(k), an evaluationfunction H_(k) associates to one evaluation domain D^(i) _(k) of D_(k) acriterion value H_(k)(D^(i) _(k),v) for a lens defined by its parametersv. Several evaluation functions are defined in the present document toevaluate directly some criteria but it has to be understood that anevaluation function can be more complex. As a first example, theevaluation function can be a mean or a sum of criterion values over anevaluation domain for criteria belonging to central and peripheralvision criteria groups. Another example of a complex evaluation functionis also given for criteria belonging to the general criteria group inthe FIG. 14.

Target values are also associated to the evaluation domains. Targetvalues are determined by the optical designer by several ways:

-   -   By using a “target lens”: for a selected criterion, target        values are computed from the target lens and are further used as        target values.    -   By using a database where target values are predetermined for a        criterion and a corresponding set of evaluation domains.    -   By using an analytic function.

Given criterion values and corresponding set of targets, the criterioncost function can be mathematically defined by:

${{J_{k}(v)} = {\sum\limits_{i = 1}^{Mk}{w_{k}^{i}*\left( {{H_{k}\left( {D_{k}^{i},v} \right)} - T_{k}^{i}} \right)^{2}}}},$

wherein T^(i) _(k) is a target value associated to an evaluation domainD^(i) _(k) and w^(i) _(k) are predetermined weights.

One can note that criteria related to visual angular field are computedfrom at least two directions (peripheral or gaze). For those criteria anevaluation domain D^(i) _(k) is composed of several directions(peripheral ray directions for a visual angular field in peripheralvision or gaze directions for a visual angular field in central vision).

Then, the cost function can be mathematically expressed by:

${J(v)} = {\sum\limits_{k = 1}^{M}{J_{k}(v)}}$

In one embodiment previous selected criteria (C₁, . . . C_(N1)) furthercomprise (C′₁, C′_(N2)) criteria belonging to the general criteriagroup.

For a criterion C′_(k) (kε[1 . . . N₂], N₂, N₂ integer superior or equalto 1) belonging to (C′₁, . . . C′_(N2))_(r) H′_(k) associates a singlecriterion value to an optical system of parameters v. The mathematicalexpression of a criterion cost function for a criterion belonging to thegeneral criteria group is then:

J′ _(k)(v)=w′ _(k)*(H′ _(k)(v)−T′ _(k))^(z),

wherein T′_(k) is the target value associated to C′_(k) and w′_(k) is apredetermined weight.

The cost function relating to all the selected criteria can then beexpressed by:

${J(v)} = {{\sum\limits_{k = 1}^{M}{J_{k}(v)}} + {\sum\limits_{k = 1}^{N\; 2}{J_{k}^{\prime}(v)}}}$

According to a non limiting example of the present invention, steps ofthe method for calculating an optical system are illustrated.

In our example, an optical designer aims at increasing the near visionobject visual angular field of a progressive lens adapted to a specificprescription (hypermetrope +4 and presbyope +2) without changing thedistributions of astigmatism and power of the lens.

The optical designer operates according to the method comprising thefollowing steps:

(i) Choice of Criteria:

The selected criteria are power in central vision (C₁), astigmatism incentral vision (C₂) and object visual angular field in central vision(C₃).

(ii) Definition of the Evaluation Domains and corresponding sets oftarget values:

For power and astigmatism, each evaluation domain is composed of onegaze direction. All the directions (α_(i),β_(j)) enabling to trace a rayentering the lens are considered: D₁=D₂={(α_(i),β_(j)), iε[1 . . . m]}.The evaluation zones comprise n*m evaluation domains. The associated setof target values are T₁=(T^(i,j) ₁) and T₂=(T^(i,j) ₂).

For object visual angular field, the evaluation zone consists of oneevaluation domain that is composed of two gaze directions: D₃={[(α, β₁),(α, β₂)]}, wherein α=31° corresponds to a value chosen for the nearvision angular field, β₁=−5° and β₂=β13° being determined according to achosen isoastigmatism line and in the direction α. The associated set oftarget value T₃ consists of one value T₃=14° is chosen.

(iii) Choice of an Initial Lens:

An initial lens v_(ini) is then determined by its parameters(coefficients of the equations of all its surfaces, index of the glassesand position of each surface relatively to each other). This lens ischosen to fit with the astigmatism and power distribution prescribed.The index of the glass is 1.5, its base curve is equal to 7 and theaddition on the front surface is 2 diopters.

(iv) Evaluation of the Cost Function:

Each criterion cost function is computed according to the correspondingset of evaluation domains and targets for said lens parameters V_(ini).

${J_{1}\left( v_{ini} \right)} = {\sum\limits_{i,j}\left( {{H_{1}\left( {D_{1}^{i,j},v_{ini}} \right)} - T_{1}^{i,j}} \right)^{2}}$${J_{2}\left( v_{ini} \right)} = {\sum\limits_{i,j}\left( {{H_{2}\left( {D_{2}^{i,j},v_{ini}} \right)} - T_{2}^{i,j}} \right)^{2}}$$\begin{matrix}{{J_{3}\left( v_{ini} \right)} = \left( {{H_{3}\left( {D_{3},v_{ini}} \right)} - T_{3}} \right)^{2}} \\{= \left( {{{{\beta \; 1} + {{Dp\_ H}\left( {\alpha,{\beta \; 1}} \right)}}} + {{{\beta \; 2} + {{Dp\_ H}\left( {\alpha,{\beta \; 2}} \right)}}} - T_{3}} \right)^{2}}\end{matrix}$

where

H₁(D^(i,j) ₁,v_(ini)) is the criterion value evaluated for theparticular gaze direction D^(i,j) ₁=(α_(i),β_(j)) with the evaluationfunction H₁ which is the classical power function.

H₂ (D^(i,j) ₂, v_(ini)) is the criterion value evaluated for theparticular gaze direction D^(i,j) ₂=(α_(i,β) _(j)) with the evaluationfunction H₂ which is the classical astigmatism function.

According to a predetermined set of weights (for example: w₁=1, w₂=1,w₃=2), the cost function is then computed:

J(v _(ini))=J ₁(v _(ini))+J ₂(v _(ini))+2*J ₃(v _(ini))

(v) Optimization:

The parameters of the lens are then modified in order to minimize thecost function.

The optimization leads to a lens v_(f) whose cost function satisfies theconvergence criterion. The lens v_(f) has exactly the same distributionof astigmatism and power as the lens v_(ini). However, the object visualangular field obtained for v_(f) is equal to 14′.

It is clear that the preceding steps do not have mandatory to beimplemented according to the order described hereinabove. It is possibleto employ other methods of optimization, and other ways of representingsurfaces differing from the method proposed.

The invention has been described above with the aid of embodimentswithout limitation of the general inventive concept. In particular thepresent invention provides a method for calculating by optimization anoptical system, the optical system being all kinds of optical lenses,particularly ophthalmic lenses, e.g. single vision (spherical, torical),bi-focal, progressive, aspherical lenses (etc).

1. A method implemented by computer means for calculating byoptimization an optical system for example an ophthalmic lens accordingto at least one criterion comprising the steps of: i. Selecting at leastone criterion among one or several of the three following criteriagroups consisting of: central vision criteria group consisting of:ocular deviation, object visual angular field in central vision, imagevisual angular field in central vision, or a variation of precedingcriteria; peripheral vision criteria group consisting of: pupil fieldray deviation, object visual angular field in peripheral vision, imagevisual angular field in peripheral vision, prismatic deviation inperipheral vision, magnification in peripheral vision, or a variation ofpreceding criteria; general criteria group consisting of lens volume,magnification of the eyes, temple shift; ii. For each selected criterionof step i.), defining: an evaluation zone comprising one or severalevaluation domains and a set of target values associated to saidevaluation domains, if said criterion of step i.) belongs to the centralor to the peripheral vision criteria groups, or a target valueassociated to said criterion of step i.), if said criterion belongs tothe general criteria group; iii. Selecting a starting optical system anddefining a working optical system to be equal to the starting opticalsystem, where the starting optical system and the working optical systemcomprise each at least two optical surfaces; iv. Evaluating for theworking optical system and for each selected criterion of step i.): aset of criterion values associated to said evaluation domains of stepii.), if said criterion of step i.) belongs to the central or peripheralvision criteria groups, a criterion value, if said criterion of step i.)belongs to the general criteria group; v. Modifying at least oneparameter of the working optical system, in order to minimize a costfunction considering target values and criterion values by repeatingstep iv.) till a stop criterion is satisfied.
 2. The method according toclaim 1, wherein the cost function is a sum over the selected criteriaof step i.) of: sums, over the evaluation domains of step ii.) ordifferences between a criterion value associated to an evaluation domainof step ii.) and the target value associated to said evaluation domainto the power of two, for criteria of step i.) belonging to the centralvision and peripheral vision criteria groups, and differences between acriterion value and a target value of step ii.) to the power of two, forcriteria of step i.) belonging to the general criteria group.
 3. Themethod according to claim 1, wherein the working optical system to beoptimized comprises at least two optical surfaces and the parameterwhich is modified is at least a coefficient of the equation of oneoptical surface of the working optical system.
 4. The method accordingto claim 1, wherein the working optical system to be optimized comprisesat least two optical surfaces and the parameters which are modified areat least the coefficients of the equations of two optical surfaces ofthe working optical system.
 5. The method according to claim 1, whereina selected criterion of step i.) belongs to the central vision criteriagroup and wherein the associated evaluation domains of step ii.)comprise at least one gaze direction, said direction being consideredwith regard to reference axes associated with the eye rotation centerand used to perform ray tracing from the eye rotation center for thecriterion evaluation.
 6. The method according to claim 1, wherein aselected criterion of step i.) belongs to the peripheral vision criteriagroup and the associated evaluation domains of step ii.) comprise atleast one peripheral ray direction, said direction being considered withregard to reference axes associated with the entrance pupil centermoving along a determined gaze direction and used to perform ray tracingfrom the entrance pupil center for the criterion evaluation.
 7. Themethod according to claim 5, wherein a selected criterion of step i.)belongs to any of: ocular deviation, pupil field ray deviation,prismatic deviation in peripheral vision, magnification in peripheralvision, and wherein the associated evaluation domains consist in onedirection.
 8. The method according to claim 5, wherein a selectedcriterion of step i.) belongs to any of object visual angular field incentral vision, image visual angular field in central vision, objectvisual angular field in peripheral vision and image visual angular fieldin peripheral vision, and wherein the associated evaluation domainscomprise of at least two directions. 9.-11. (canceled)
 12. The methodaccording to claim 1, wherein the cost function J is mathematicallyexpressed according to:${{J(v)} = {{\sum\limits_{k = 1}^{N\; 1}{\sum\limits_{i = 1}^{Mk}{w_{k}^{i}*\left( {{H_{k}\left( {D_{k}^{i},v} \right)} - T_{k}^{i}} \right)^{2}}}} + {\sum\limits_{k = 1}^{N\; 2}{w_{k}^{\prime}*\left( {{H_{k}^{\prime}(v)} - T_{k}^{\prime}} \right)^{2}}}}},$wherein: k and i are integer variables, N₁ is an integer superior orequal to 1 and represents the number of selected criteria of step i.)belonging to the central vision and peripheral vision criteria groups;N₂ is an integer superior or equal to 1 and represents the number ofselected criteria of step i.) belonging to the general criteria group;M_(k) is an integer superior or equal to 1 and represents the number ofevaluation domains of step ii.) for a criterion of step i.) belonging tothe central vision or peripheral vision criteria groups of index k; v isdefining the working optical system parameters; W^(i) _(k) are theweights associated to a criterion of step i.) belonging to the centralvision or peripheral vision criteria groups of index k and to anevaluation domain of step ii.) of index i; w′_(k) is the weightassociated to a criterion of step i.) belonging to the general criteriagroup of index k D^(i) _(k) is an evaluation domain of step ii.) ofindex i of an evaluation zone associated to a criterion belonging to thecentral vision or peripheral vision criteria groups of index k; H_(k)associates a criterion value to a criterion of step i.) belonging to thecentral vision or peripheral vision criteria groups of index k anevaluation domain of step ii.) D^(i) _(k) and an optical system definedby its parameters v; H′_(k) associates a criterion value to a criterionof step i.) belonging to the general criteria group of index k and anoptical system defined by its parameters v; T^(i) _(k) is a target valueof index i of the set of target values associated to an evaluationdomain of step ii.) D^(i) _(k), of a criterion belonging to the centralvision or peripheral vision criteria groups of index k; T′_(k) is thetarget value associated to a criterion belonging to the general criteriagroup of index k.
 13. A method of manufacturing an optical system, themethod comprising the steps of: calculating by optimization the opticalsystem according to claim 1, and surface machining of at least oneoptical surface according to said optical system.
 14. A computer programproduct comprising one or more stored sequence of instruction that isaccessible to a processor and which, when executed by the processor,causes the processor to carry out the steps of claim
 1. 15. Acomputer-readable medium carrying one or more sequences of instructionsof the computer program product of claim
 14. 16. The method according toclaim 5, wherein a selected criterion of step i.) is defined either by avariation of a criterion of step i.) belonging to the central visioncriteria group or by a variation of a criterion of step i.) belonging tothe peripheral vision criteria group.
 17. The method according to claim1, wherein the method for calculating an optical system furthercomprises astigmatism criterion in central vision and/or power criterionin central vision.
 18. The method according to claim 1, wherein theoptical system is a progressive addition lens and the method forcalculating an optical system further comprises add power criterion incentral vision.
 19. The method according to claim 6, wherein a selectedcriterion of step i.) belongs to any of: ocular deviation, pupil fieldray deviation, prismatic deviation in peripheral vision, magnificationin peripheral vision, and wherein the associated evaluation domainsconsist in one direction.
 20. The method according to claim 6, wherein aselected criterion of step i.) belongs to any of object visual angularfield in central vision, image visual angular field in central vision,object visual angular field in peripheral vision and image visualangular field in peripheral vision, and wherein the associatedevaluation domains comprise of at least two directions.
 21. The methodaccording to claim 6, wherein a selected criterion of step i.) isdefined either by a variation of a criterion of step i.) belonging tothe central vision criteria group or by a variation of a criterion ofstep i.) belonging to the peripheral vision criteria group.